Positron Emission Tomography (PET) is an available specialized imaging technique that uses tomography to computer-generate a three-dimensional image or map of a functional process in the body as a result of detecting gamma rays when artificially introduced radionuclides incorporated into biochemical substances decay and release positrons. Analysis of the photons detected from the deterioration of these positrons is used to generate the tomographic images which may be quantified using a color scale to show the diffusion of the biochemical substances in the tissue indicating localization of metabolic and/or physiological processes. For example, radionuclides used in PET may be a short-lived radioactive isotope such as Flourine-18, Oxygen-15, Nitrogen-13, and Carbon-11 (with half-lives ranging from 110 minutes to 20 minutes). The radionuclides may be incorporated into biochemical substances such as compounds normally used by the body that may include, for example, sugars, water, and/or ammonia. The biochemical substances may then be injected or inhaled into the body (e.g., into the blood stream) where the substance (e.g., a sugar) becomes concentrated in the tissue of interest where the radionuclides begin to decay emitting a positron. The positron collides with an electron producing gamma ray photons which can be detected and recorded indicating where the radionuclide was taken up into the body. This set of data may be used to explore and depict anatomical, physiological, and metabolic information in the human body. While alternative scanning methods such as Magnetic Resonance Imaging (MRI), Functional Magnetic Resonance Imaging (fMRI), Computed Tomography (CT), and Single Photon Emission Computed Tomography (SPECT) may be used to isolate anatomic changes in the body, PET may use administrated radiolabeled molecules to detect molecular detail even prior to anatomic change.
PET studies in humans are typically performed in either one of two modes, providing different sets of data: whole body acquisition whereby static data for one body sector at a time is sequentially recorded and dynamic acquisition whereby the same sector is sequentially imaged at different time points or frames. Dynamic PET studies collect and generate data sets in the form of congruent images obtained from the same sector. These sequential images can be regarded as multivariate images from which physiological, biochemical and functional information can be derived by analyzing the distribution and kinetics of administrated radiolabeled molecules. Each one of the images in the sequence displays/contains part of the kinetic information.
Due to limitations in the amount of radioactivity administered to the subject, a usually short half-life of the radionuclide and limited sensitivity of the recording system, dynamic PET images are typically characterized by a rather high level of noise. This together with a high level of non-specific binding to the target and sometimes small differences in target expression between healthy and pathological areas are factors which make the analysis of dynamic PET images difficult independent of the utilized radionuclide or type of experiment. This means that the individual images are not optimal for the analysis and visualization of anatomy and pathology. One of the standard methods used for the reduction of the noise and quantitative estimation in dynamic PET images is to take the sum, average, or mean of the images of the whole sequence or part of the sequence where the specific signal is proportionally larger. However, though sum, average, or mean images may be effective in reducing noise, these approaches result in the dampening of the differences detected between regions with different kinetic behavior.
Another method used for analysis of dynamic PET images is kinetic modeling with the generation of parametric images, aiming to extract areas with specific kinetic properties that can enhance the discrimination between normal and pathologic regions. One of the well established kinetic modeling methods used for parameter estimation is known as the Patlak method (or sometimes Gjedde method). The ratio of target region to reference radioactivity concentration is plotted against a modified time, obtained as the time integral of the reference radioactivity concentration up to the selected time divided by the radioactivity concentration at this time. In cases where the tracer accumulation can be described as irreversible, the Patlak graphical representation of tracer kinetics becomes a straight line with a slope proportional to the accumulation rate. This method can readily be applied to each pixel separately in a dynamic imaging sequence and allows the generation of parametric images representative of the accumulation rate. Alternative methods for the generation of parametric images exist; based on other types of modeling, e.g. Logan plots, compartment modeling, or extraction of components such as in factor analysis or spectral analysis. Other alternatives such as population approaches, where an iterative two stage (ITS) method is utilized, have been proposed and studied and are available.
A notable problem when using kinetic modeling is that the generated parametric images suffer from poor quality while the images are rather noisy. This indicates that kinetic modeling methods such as Reference Patlak, do not consider any Signal-to-Noise-Ratio (SNR) optimization during the measurement of physiological parameters from dynamic data.
Dynamic PET images can also be analyzed utilizing different multivariate, statistical techniques such as Principal Component Analysis (PCA), which is one of the most commonly used multivariate analysis tools. PCA also has several other applications in the medical imaging field such as, for example, in Computed Tomography (CT) and in functional Magnetic Resonance Imaging (fMRI). This technique is employed in order to find variance-covariance structures of the input data in unison to reduce the dimensionality of the data set. The results of the PCA can further be used for different purposes e.g. factor analysis, regression analysis, and used for performing preprocessing of the input/raw data.
The conventional use of PCA indicates a data driven technique which has difficulty in separating the signal from the noise when the magnitude of the noise is relatively high. The presence of variable noise levels in the different PET images dramatically affects the subsequent multivariate analysis unless properly handled otherwise PCA will emphasize noise and not the regions with different kinetics. For this reason, using PCA on dynamic PET images is not an optimal solution.